Question

The profit function for a product is given by p(x) = –4x 28x –40, where x is the number of products sold. Both the number of products and the profit are in thousands. a) Determine how many items must be sold for the company to break-even. b) Determine how many items must be sold for the company to make a profit of eight thousand dollars?

Answer 1

To find the break-even point, solve the profit function equation for x=0. To find the number of items required to make a profit of $8,000, set the profit function equation equal to $8,000 and solve for x.

Step-by-step explanation:

To determine the break-even point, the profit function equation p(x) should be set to zero and solved for x. In this case, the equation is: p(x) = -4x^2 + 28x - 40 = 0. Solve this quadratic equation for x to find the break-even point.

To determine the number of items that must be sold for the company to make a profit of eight thousand dollars, set the profit function equation p(x) equal to $8,000 and solve for x. In this case, the equation is: p(x) = -4x^2 + 28x - 40 = 8. Solve this quadratic equation for x to find the number of items required to make a profit of $8,000.